3D Constrained Inversion For Gravity And Magnetic Data

Gravity and magnetic prospecting, as cheap and fast exploration approaches, have been widely applied in many fields such as geological survey, oil and gas exploration, solid mineral resources prospecting, and hydrological, engineering and environmental investigation. While the recovery of physical properties distributions from the gravity and magnetic data enables to visually outline the spacial shapes and distributed features of the complex gravity and magnetic field sources, which, therefore, becomes an important work for the procession and interpretation of gravity and magnetic data and also it is a research focus for the inversion of gravity and magnetic data in recent years. However, the difficulties including the large computational load, low inversion resolution, and serious non-uniqueness problem for the inversion of gravity and magnetic data limit the application and development of gravity and magnetic methods. In this thesis, to improve the computational efficiency and inversion quality, I studied the methods of constrained inversion for gravity and magnetic data on the basis of three aspects:model constraints, data constraints and the improvement of inversion strategies. The main research contents and conclusions are as following:(1) I achieved the 3D rapid inversion of gravity and magnetic data by use of preconditioned conjugate gradient (PCG) method. The conjugate gradient (CG) is one of the most effective methods for solving the large linear equations because the CG algorithm searches for the extremum point along the conjugate direction which is composed of gradient direction from the starting point and it would be converged after finite iterations. Moreover, all operations of CG are based on vector operation, so that the vector variables in the iterative processes can be repeatedly used, which helps to reduce the loads of computational time and memory storage spaces. The preconditioner in PCG decided by the distances between the observation points and the mesh cells improves the condition number of the matrix equation and hence promotes the convergence rate of the CG method.(2) I achieved the 2D forward and inverse modeling of gravity and magnetic data on rugged observation surface using constraint Delaunay triangulation (CDT). The regular rectangular and tetrahedral grid discretization is prevalent in the inverse modeling for potential field data. But this subdivision strategy performs lower precision to represent the rugged observation surface. In this thesis, I evaluated a non-structured discretization method in which the subsurface with rolling terrain is divided into numbers of Delaunay triangular cells and each mesh has the uniform physical property distributions. The gravity and magnetic anomalies of a complex-shaped anomalous body are represented as the summaries of the single anomaly produced by each triangle field source. When inverting for the potential field data, I used PCG to iteratively solve the matrix minimization equations. The discretization of CDT provides an useful approach of computing and inverting the potential field data on the situations of undulate topography and complicated objects. The method also can be extended to the 3D inversion of potential fields if dividing the subsurface into numbers of tetrahedron cells.(3) I achieved the 3D magnetization vector inversion (MVI) in the presences of significant remanent magnetization and self-demagnetization. In the inversion and interpretation of magnetic data, it is meaningful to recover the distributions of total magnetization vector (TMV) since the remanence and self-demagnetization produce the similar responses that alter their magnitude and direction. I evaluated and compared three MVI approaches:simultaneously inverting the TMV’s three orthogonal components (MMM); simultaneously inverting the TMV’s magnitude, inclination and declination (MID); and orderly inverting the magnetization intensity, inclination and declination based on the transformed magnitude magnetic anomaly (M-ID). The inversion results revealed that the isochronous MMM inversion aggravates the geophysical non-uniqueness problem and MID performs low stability of convergence due to the strong dependence on the starting models. While the sequential M-ID shows superior stability and precision of inverting the magnetization intensity and direction by making successive use of the amplitude and phase information of the magnetic anomaly. Finally, the achieved TMV distributions help us to investigate the influence of remanent magnetization and to recover the physical property distributions for high susceptibility when the self-demagnetization effect is not negligible, which offers a new idea to research the remanence and self-demagnetization.(4) I summarized the generalized model-constrained based inversion of gravity and magnetic data. The generalized model constraint is the most extensive constrained inversion method of gravity and magnetic data, including classical Tikhonov regularization inversion, as well as the absolute constraint, inequality constraint, reference model constraint inversion. For different prior information like the drillhole, geological and other geophysical data, I interpolated the prior information and then regarded them as an initial model or reference model to carry out the constrained inversion. The initial model constrained inversion shows good convergence, but the constraint effect is inferior to reference model constrained inversion. The reference model constrained inversion depends on the regularization factor and has slower speed of convergence. The results demonstrate that constrained inversion under prior information more accurately reflects the distributions of field sources.(5) I carried out the data-constrained based constrained inversion for gravity and magnetic data. Data constraint means the constraint of different geophysical fields, namely the joint inversion of geophysical fields, including the joint inversion of gravity and magnetic data, gravity and seismic data, electrical and magnetic data, borehole and surface data, surface and airborne data, and so on. I implemented the joint inversion of surface and three-component borehole magnetic data. The inversion results concluded that the data-constrained joint inversion can more accurately recover the distributions of field sources. The joint inversion between the different geophysical fields is an important strategy to implement constrained inversion.(6) I proposed the sparse inversion of gravity and magnetic data based on the l0-norm constraints. Traditional approaches inverting for potential field data are based on the observation data and model parameters constrains of l2-norm. However, the recovered physical properties distributions are prone to be smooth and the low resolution leads to the unclear physical properties boundaries. To improve the inversion resolution, I presented a sparsity inversion method of orthogonal matching pursuit (OMP) optimizing l0-norm model parameters constrains. Because the potential field data can be linearly combined by column vectors of sensitive matrix, I employ the column vector of sensitive matrix to be an atom and the whole sensitive matrix constitutes a over-complete atom dictionary of OMP. Simultaneously, I select the most correlative column vector with observed gravity and magnetic anomalies as the optimal atom to match. The OMP can rapidly invert for the sparse distributions of physical properties and can recover the sharply physical properties boundaries and promote the inversion resolution.(7) I proposed the discrete inversion of gravity and magnetic data based on the non-linear stochastic algorithm of swarm intelligence optimization. Compared with the linear inversion method, non-linear stochastic algorithm is easier combined with the prior information. Swarm intelligence optimization is an effective stochastic inversion algorithm. In this thesis, taking the ant colony optimization (ACO) algorithm as an example, I firstly achieved the absolute constrained inversion by interfering the movements of ant colony. In addition, when recovering the physical properties distributions, the physical properties of mesh cells are given some discrete values such as 0 and 1, where the 0 represents the cell does not have density or susceptibility contrast, while the 1 represented the cell has density or susceptibility contrast. This binary representation method is an effective measurement to relieve the geophysical non-uniqueness according to reducing the solution space. It is suitable for the situations that the target bodies such as sedimentary iron ores and granite rocks have obvious and steady physical properties contrasts.